Student[NumericalAnalysis]
IsMatrixShape
Check whether a matrix is a certain shape or not
Calling Sequence
Parameters
Description
Notes
Examples
IsMatrixShape(A, shape)
A
-
Matrix
shape
name; must be one of diagonal, strictlydiagonallydominant, diagonallydominant, hermitian, positivedefinite, symmetric, triangular[upper], triangular[lower], or tridiagonal
The IsMatrixShape command verifies whether the matrix A is a certain "shape".
The only types of "shapes" that the IsMatrixShape command can verify are:
Diagonal : shape = diagonal
Strictly diagonally dominant : shape = strictlydiagonallydominant
Diagonally dominant : shape = diagonallydominant
Hermitian : shape = hermitian
Positive definite : shape = positivedefinite
Symmetric : shape = symmetric
Upper or lower triangular : shape = triangular[upper] or shape = triangular[lower], respectively
Tridiagonal : shape = tridiagonal
If neither upper nor lower is specified, the triangular option defaults to triangular[upper].
The Student[NumericalAnalysis] subpackage's definition of positive definiteness is as follows.
A complex n-by-n matrix A is positive definite if and only if A is Hermitian and for all n-dimensional complex vectors v, we have 0<ℜvH·A·v, where ℜ denotes the real part of a complex number.
A real n-by-n matrix A is positive definite if and only if A is symmetric and for all n-dimensional real vectors v, we have 0<vT·A·v.
To check another "shape" that is not available with the Student[NumericalAnalysis][IsMatrixShape] command see the general IsMatrixShape command.
withStudentNumericalAnalysis:
A≔Matrix2,−1,0,0,−1,2,−1,0,0,−1,2,−1,0,0,−1,2
A≔2−100−12−100−12−100−12
B≔Matrix−1,0,0,0,−1,2,0,0,1,−1,−3,0,−1,1,−1,4
B≔−1000−12001−1−30−11−14
C≔Matrix3,−I,1,0,I,4,2I,0,1,−2I,5,1,0,0,1,4
C≔3−I10I42I01−2I510014
IsMatrixShapeA,diagonal
false
IsMatrixShapeA,strictlydiagonallydominant
IsMatrixShapeA,diagonallydominant
true
IsMatrixShapeC,hermitian
IsMatrixShapeA,positivedefinite
IsMatrixShapeB,positivedefinite
IsMatrixShapeC,positivedefinite
IsMatrixShapeA,symmetric
IsMatrixShapeB,triangularupper
IsMatrixShapeB,triangular
IsMatrixShapeLinearAlgebra:-TransposeB,triangular
IsMatrixShapeB,triangularlower
IsMatrixShapeA,tridiagonal
See Also
Student[NumericalAnalysis][ComputationOverview]
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